Wittgenstein on Quantum Mechanics

Wittgenstein starts out in Tractatus (1921):

• The world is the totality of facts, not of things.
• We make to ourselves pictures of facts.
• In order to tell whether a picture is true or false, we must compare it with reality.

Wittgenstein followed the development of Quantum Mechanics QM with a critical mind stating that physicists should be not occupied be with "interpretations" QM because, as stated in Lectures on the Foundations of Mathematics (1939) and in statements attributed to him:

• Physics is not a theory but the description of facts by means of mathematical symbols.  
• If people did not talk nonsense about quantum theory, there would be nothing remarkable about it.
• Quantum mechanics does not explain anything; it only describes phenomena by means of a calculus.
• When people say that something is "explained" by quantum mechanics, what they mean is that we can calculate it.
• A good model in physics is not one that shows us how nature really is, but one that gives us a clear method of description.

Concerning the probabilistic nature of QM, as opposed to classical physics:

• Physicists say: the laws of quantum mechanics are probabilistic. But probability is not something that exists in nature, like a gas or a liquid. It is a measure we use — a form of description.
• To say "nature behaves probabilistically" is as nonsensical as to say "nature obeys logic".
• We do not describe how nature is — we construct a grammar in which our descriptions make sense.
• The physicists say: at the atomic level there is no causality.
But what are they describing when they say this? A new form of experience?
No. They are proposing a new rule for the use of words like "cause"

W insists that “probability” is a rule of representation — part of the grammar of our scientific language. It tells us how we may speak about phenomena, not what the world is like.

Summary: We read that W like Einstein was critical to an idea that "atoms play dice" which is central to Quantum Mechanics in its main Bohr-Born-Heisenberg Copenhagen "interpretation". W emphasises the role of mathematics as a language/grammar to describe physics rather than to show what physics is. W makes a distinction between classical physics which can be described in a meaningful language rooted in our experience, and QM asking for a new language with new meaning for which the experience is lacking. W would have been happy to meet Real Quantum Mechanics using the same language as classical physics. 

Here is my idea of Wittgenstein's worldview as basically classical physics - rational mechanics to be used as follows:

• Formulate a mathematical model of the World which is meaningful and computable.
• Give input to the model and let it after computation respond by output and compare with reality.
• Use the model as language to speak about/with the World.  

To make QM serve this role is complicated since it has no clear physical meaning nor is computable. 

PS One can make the following distinction as concerns mathematical models/theories:

1. The model is a (more or less complete) representation of the real world.
2. The model is a representation of an imagined world which can be real (more or less).
3. The model is a representation of an imagined world which cannot be real.   

 Here 1. makes the map equal to the territory. while 2. could be W's view, and QM falls into 3. 

Modern Physics: Imagination = Reality: Hyperreality

Modern physics started in 1900 with Planck's mathematical "trick" of imagining a "smallest quantum of energy" to derive Planck's Law of blackbody radiation about an imagined "empty cavity" filled with "degrees of freedom". 

Einstein followed up in 1905 imagining himself riding on a wave of light at the speed of light, or watching a train pass a station with half the speed of light. 

The imagination expanded in 1926 into describing a World filled with "particles" by a complex-valued  "wave function" $\Psi (X,t)$ with "coordinates" $X$ ranging over a "configuration space" with a separate 3d Euclidean space coordinate identifying the position at time $t$ of each "particle" of the World. 

The wave function $\Psi (X,t)$ was viewed to carry "all there is to know" about the World however in a cryptic form which needed unwinding to make sense. 

The evolution in time of $Psi (X,t)$ as function of $X$ was given as solution to a Schrödinger equation. This was the birth of Quantum Mechanics as the foundation of modern physics.

Key question: What is the physical meaning of the wave function $\Psi(X,t)$ with $X$ ranging over configuration space? 

In 1927 Max Born suggested:

• $\vert\Psi (X,t)\vert^2$ is the probability that the particle configuration of World at time $t$ is given by $X$. 
• $\Psi (X,t)$ does not describe an actual configuration $X$ but only a possible configuration. 

This was quickly accepted because it appeared as the only possibility, which decided the path of modern physics to follow. 

The step from actual to possible configuration was a step from firm classical ground into something completely different. A grandiose step worthy a modern physicist. 

Classical physics seeks to describe the actual evolution in time of a physical system from some given initial state typically by time-stepping computational procedure. For each given initial state a final state is computed. But it is out of question to consider all possible initial states because it requires infinite computational work. 

But going from actual to possible as in QM involves all initial values, which means the $\Psi (X,t)$ with $X$ ranging over configuration space is uncomputable. This means that the goal of describing the World by a wave function $\Psi (X,t)$ cannot be reached because the required computational work cannot be created.

How are modern physicists handling the impossible situation they have created? 

The only possibility appears to be to give up the classical physics distinction between a World of specific real configurations evolving in time by some form of computation, and a Mind of an Observer which follows  the evolution but is also free to invent whatever comes to mind. By replacing computable by "thinkable" it is thus possible to let the Mind of an Observer be part of the World and so get around limitations of reality.

Does it work? What happens if we give up the distinction between observer and observed, or painter and model as depicted by Picasso? 

It opens to self-interaction which is a delicate subject. Is imagined reality also reality? A classical physicist would say no, and a modern yes while having to deal with the infinities of QED.

Baudrillard describes imagined reality conceived as reality as hyperreality as an (potentially dangerous)  aspect of modern society. It seems that QM is concerned with hyperreality rather than reality. See next post.

Quantum Mechanics as Thought Experiment as Hyperreality

Modern physics today faces a credibility crisis from lack of realism introduced 100 years ago in the form  of Standard Quantum Mechanics StdQM described by Schrödinger's equation in terms of a multi-dimensional wave function without real ontological physical meaning, only a statistical epistemological meaning in the mind of an Observer. 

This represents a fundamental break with classical physics, where the Observer has no active role to play. 

For 100 years it has been possible to play a double game shifting between ontology (what is in the real world) and epistemology (what is in the mind of an Observer) to cover up the lack of physical meaning of the multi-d wave function. 

To illustrate this state of affairs, consider a Hydrogen atom with one electron surrounding a proton at $x=0$ with the following wave function depending on a 3d Euclidean space coordinate describing the ground state

• $\psi (x)=\frac{1}{\sqrt{\pi}}\exp(-\vert x\vert )$. 

StdQM gives the wave function the following interpretation: 

• $\psi^2 (x)$ is the probability of finding the electron at position $x$. 
• $\psi^2 (x)$ is a probability density.
• Here the meaning "of finding" is crucial?
• Is it possible to experimentally "find" an electron at a particular point $x$?
• No, this is impossible because an electron is not a classical particle.
• There is no real experiment expressing "finding an electron a particular point in space".
• The only possibility is to give "finding" the meaning of a thought experiment. 
•  $\psi^2 (x)$ is the probability density of imagining finding an electron at position $x$.  

RealQM as an alternative to StdQM gives a different meaning in terms of classical deterministic physics:

• $\psi^2 (x)$ is an electron charge density in $x$ as real physics. 
• No probability is involved. No need to give $\psi^2 (x)$ any other meaning than charge density.

The argument extends to atoms with more than one electron. For an atom with $N$ electrons, the StdQM wave function $\psi (x_1, x_2,...,x_N)$ depends on $N$ 3d spatial variable $x_1,...,x_N$ and 

• $\psi^2 (x_1,x_2,...,x_N)$ is the probability of finding electron 1 at $x_1$, electron 2 at $x_2$, electron N at $x_N$. 
• This is again only possible as a thought experiment. 

The electron configuration of RealQM is the result of an energy minimisation over non-overlapping one electron charge densities without need of probability.

In short, StdQM is unphysical in the sense of not connecting theory to real experiments, but instead to imagined thought experiments. 

Thought experiments can be illuminating if thoughts can be transformed to reality. If not thought experiments stay in the head of an Observer and the connection to reality is compromised.  This is the case with StdQM and the result after 100 years is a severe crisis of credibility. Sum up:

• Classic: Independent Reality exists outside Observer. Observer is passive. RealQM
• Modern: Observer active. Reality is what goes on in the mind of the Observer. StdQM 

This connects to the idea of hyperreality used by Baudrillard to capture an important aspect of modern digital society: 

• Mathematical model describes reality which does exist: RealQM: Reality: Classical physics.
• Mathematical model describes a reality which does NOT exist: StdQM: Hyperreality: Modern Physics.

    

No Nobel Prizes to Theoretical Quantum Mechanics and General Relativity!

Here is a perspective on the previous post:

Let us consider how the Nobel Committee has awarded work of major theoretical nature on Quantum Mechanics as the foundation of modern physics: 

1932 Werner Heisenberg: Matrix mechanics, 1933 Erwin Schrödinger: Schrödinger wave equation, 1933 Paul Dirac: Dirac equation = Relativistic wave equation, 1954 Max Born: Statistical interpretation of wave function, which can be complemented with very preliminary  1918 Max Planck: Quantum of energy/action $h\nu$ 1921 Albert Einstein: Quantum of light $h\nu$ = photon. There are several Prizes to experimental work connecting to "quantum",  but none to any of the fundamentally different interpretations seeking to specify the physical meaning of Schrödinger/Dirac wave equation and wave functions including: Copenhagen Bohr-Born-Heisenberg 1927, Bohmian mechanics 1952, Many-Worlds 1957, Collapse Models 1990-2000. This means that through the 100 years history of QM as the foundation of modern physics, the physical meaning of the theory is still completely open. The common agreement is that "QM works" exceedingly well, so amazingly well that there not a single experiment not in full agreement with QM, while it is also agreed that "nobody knows why". None of the above interpretations has shown to be worthy of a prize, indicating that they are all wrong.  So the last time a Prize was awarded to QM including theory, was to Born in 1954 for his statistical interpretation in 1927, while this was the reason he was left out in 1932-33.  Modern physics is based on the theories of QM + General Relativity GR. It is very remarkable that no Prize has been given to a discovery of the physical meaning of either the "quantum" of QM or the "curved space-time" of GR.  It is natural to connect the present crisis of theoretical physics to a growing feeling of lack credibility coming from lack of Prize to theory over a very long time.  Recall also that an experiment without theory is blind. An experiment must be interpreted to have a meaning. A number or blip on a screen says nothing in itself.  Recall that all trouble comes from the generalisation of Schrödinger's equation for the Hydrogen atom with is wave function representing its one electron charge density in concrete physical terms, to atoms with more than one electron in terms of a multi-dimensional wave function without physical representation. Real Quantum Mechanics offers a different generalisation with concrete charge density representation. A Prize to RealQM is not unthinkable...

Nobel Prize in Physics 2025 vs Ukulele Vibrating Strings

The 2025 Nobel Prize in Physics was awarded to John Clarke, Michel H. Devoret, and John M. Martinis 

• for experiments that revealed quantum physics in action,
• particularly their pioneering work in demonstrating that quantum mechanical effects can manifest at a macroscopic (larger-than-atomic) scale.

The general idea is that the microscopic world of quantum mechanics contains wonderful subtle small-scale phenomena of superposition and entanglement not present in the macroscopic world where averaging destroys small scales. 

The idea of quantum computing is to use quantum states in superposition to perform computations in parallel and so reach entirely new levels of computational power. 

The idea of the Nobel Prize is to upscale quantum capacities for parallel computing to larger scales allowing more efficient error control and input/output.  

Upscaling of microscopics to macroscopics is opposite to the downscaling of mechanical calculators to microprocessor of computers behind the digital revolution.  

There is a clear connection to recent blog posts asking to what extent the microscopic quantum world is different from the macroscopic world, with the conclusion that the difference is not so big after all. 

If so, it should be possible to find the wonderful quantum effects like superposition directly on familiar macro-scales like a vibrating string. This opens to use e g an ukulele as efficient computing device in room temperature, instead of super-conduction at very low temperatures. 

Mystery of Planck's Constant Revealed

This is a clarification of this post on the physical meaning of Planck's constant $h$ and so of Quantum Mechanics QM as a whole. The basic message is that the numerical value of $h=6.62607015\times 10^{-34}$ Jouleseconds is chosen to make Planck's Law fit with observation and that this value is then inserted into Schrödinger's equation to preserve the linear relation between energy and frequency established in Planck's Law. 

Quantum Mechanics is based on a mysterious smallest quantum of energy/action $h$ named Planck's constant, which was introduced by Planck in 1900 as a "mathematical trick" to make Planck's Law of blackbody radiation fit with observations of radiation energy from glowing bodies of different temperatures. 

The mysterious Planck's constant  $h$ appears in Planck's Law in the combination $\frac{h\nu}{kT}$ where $\nu$ is frequency, $k$ is Boltzmann's constant and $T$ temperature with $kT$ a measure of energy (per degree of freedom) from thermodynamics. In particular  

•  $\nu_{max}=2.821\frac{kT}{h}$                   (*)

shows the frequency of maximal radiation intensity referred to as Wien's Displacement Law, which also serves as a cut-off frequency with quick decay of radiation intensity for frequencies $\nu >\nu_{max}$.  

If we translate (*) to wave length we get a corresponding smallest wave length 

• $\lambda_{min}= 0.2015\frac{hc}{kT}=\frac{0.0029}{T}$ meter
• $\lambda_{min} \approx 10^{-5}$m for $T=300$ K 
• $\lambda_{min} \approx 5\times 10^{-7}$m for $T=5778$ K (Sun)

We see that smallest wave length is orders of magnitude bigger that atomic size of $10^{-10}$ m, which tells that blackbody radiation is a collective wave phenomenon involving many atoms per radiated wave length.

Summary: 

• Planck's constant $h$ serves the role of setting a peak frequency scaling with temperature $T$ with corresponding smallest wave length scaling with $\frac{1}{T}$.
• The smallest wave length is many orders of magnitude bigger than atomic size showing blackbody radiation to be a collective wave phenomenon involving coordinated motion of many atoms. 
• Planck's constant $h$ thus has a physical meaning of setting a smallest spatial resolution size scaling with $\frac{1}{T}$ required for coordinated collective wave motion supporting radiation. 
• Higher temperature means more active atomic motion allowing smaller coordination length. 
• The standard interpretation of $h$ as smallest quanta of energy lacks physical representation.
• Connecting $h$ to coordination length is natural and gives $h$ a physical meaning without mystery. 
• Formally h = energy x time = momentum x length representing Heisenbergs Uncertainty Relation with h connecting to spatial resolution. Formally $E=h\nu=pc$ and so $h=p\lambda$.   

PS Recall that Schrödinger's equation for atoms and Maxwell's equations for light covers a very wide range of phenomena in what is referred to as a semi-classical model as half-quantum + half classical. In this model light is not quantised and there are no photons to worry about. The above meaning of $h$ from Planck's Law is understandable. The mystery is restored in Quantum Electro Dynamics QED where Maxwell's equations are replaced by the relativistic Dirac's equations and particles/photons appear as quantised excitations of fields. QED is way too complicated to be used for the wide range covered by QM and so is reserved for very special geometrically simplified situations. 

The Physical Meaning of Planck's Constant $h$

Planck's constant $h$ appears in several different contexts in quantum physics including 

1. Planck's Law of blackbody radiation.
2. Schrödinger's Equation SE describing the spectrum of the Hydrogen atom. 

Here 1. involves collective behaviour of atoms, while 2. concerns one atom. The standard view is that the double appearance of $h$ in two fundamentally different contexts is an expression of a deep connection in a mysterious quantum world, which cannot be understood.  

Let us see if we can uncover some the mystery. We recall from this post  that $h$ was introduced by Planck in 1900 to make Planck's Law fit with observation, specifically in a high frequency cut-off factor $C(\alpha )$ with $\alpha =\frac{h\nu}{kT}$ where $\nu$ is frequency, and $k$ as Boltzmann's constant combined with temperature $T$ into $kT$ serves as an energy per degree of freedom in thermodynamics.  For $h\nu << kT$ then $C(\alpha ) =1$ and for $h\nu >kT$, $C(\alpha )$ decays to zero. The quantity $h\nu$ is thus compared to the elementary energy $kT$ and so $h\nu$ is referred to as a basic quantum of energy $E=h\nu$ connected to the frequency $\nu$. This is a linear relation and $h$ is the constant of proportionality between energy and frequency. 

Energy $E$ is thus connected to frequency $\nu$ by $E=h\nu$ with physical meaning of setting the high-frequency cut-off in Planck's Law in relation to $kT$.  This explains the function of $h$ in 1. as serving in high frequency cut-off. High-frequency connects to small-wavelength which connects to spatial resolution. Wien's displacement law takes the form $\nu \approx \frac{k}{h}T$ with linear scaling between frequency and temperature as measure of energy.  We see that $h$ appears in a high-frequency threshold condition scaling with $T$ which gives $h$ a physical meaning but not as measure of physical quantity representing some smallest quantum of energy $h\nu$. Threshold condition and not physical quantity.  

We now turn to 2. recalling Schrödinger's Equation SE with $H$ a Hamiltonian:

• $ih\frac{\partial\psi}{\partial t}+H\psi =0$

with solution $\exp (i\frac{E}{h}t)\Psi$ where $\Psi$ is an eigenfunction satisfying $H\Psi =E\Psi$ with $E$ an eigenvalue as energy. We see frequency $\nu =\frac{E}{h}$ with thus $E=h\nu$. We thus see that SE is constructed to carry a linear relation between energy and frequency, more specifically the relation $E=h\nu$. Notice that temperature $T$ does not appear in SE, only in the context of blackbody radiation as collective behaviour.

We understand the value of $h=6.62607015\times 10^{-34}$ Jouleseconds is chosen to make Planck's Law fit with observation as concerns high frequency cut-off based on $h\nu$ scaling linearly with frequency $\nu$, and with $T$ in Wien's displacement law.. 

Once the value of $h$ was determined to fit 1. with linear scaling of energy vs frequency as $E=h\nu$, that value of $h$ was inserted into SE with the effect of preserving the linear scaling of energy vs frequency as $E=h\nu$. The appearance of $h$ is SE was not due to a miraculous intervention of Nature, but simply the effect of putting it in by the design of SE. 

Summary: 

1. The value of $h$ as conversion factor between energy and frequency as $E=h\nu$ in a linear relation, is set to make Planck's Law fit with observation. 
2. That value of $h$ is then inserted by design into SE to keep the $E=h\nu$ linear relation between energy and frequency. 
3. The design is elaborated by connecting a one electron energy jump $E$ to emission/absorption of one photon of frequency $\nu$ determined by $\nu =\frac{E}{h}$ as the mechanism behind the spectrum of Hydrogen.
4. In short: The appearance of  $h$ is SE is not deep mystery, but simply the design of SE.  
5. Is the fact that SE describes the observed spectrum of Hydrogen a mystery? Not with charge density representation of the wave function solution to SE, in which case SE has classical continuum mechanical form of a vibrating elastic body and as such not a mystery. 
6. Extension to atoms with more than one electron presents new questions to be answered differently by Standard QM and RealQM.

Einstein vs Lorentz, Planck and Bohr: Tragedy

Modern physics as relativity theory + quantum mechanics was born out of two misconceptions formed in the mind of the young Einstein as patent clerk in Bern in 1905 with little scientific training, but strong ambition to contribute to the emerging modern physics of  

1. Blackbody radiation.
2. Photoelectricity. 
3. Apparent absence of a unique aether carrying electromagnetic waves.  

In 1900 Planck had derived Planck's Law of blackbody radiation based on a smallest quantum of energy $h\nu$ connected to radiation/light of frequency $\nu$ with $h=6.55\times 10^{-34}$ Jouleseconds named Planck's constant. Planck did not assign any physical meaning to the smallest quantum $h\nu$ and viewed it simply as a "mathematical trick" used to derive Planck 's Law. 

In one of Einstein's 5 articles from the "miraculous year" 1905, Einstein assigns the quantum $h\nu$ a physical meaning as the energy of a "photon" as a "light particle" in a heuristic explanation of 2. Einstein thus did what Planck had said does not make any sense. In 1926 the mysterious quantum $h\nu$ appeared in Schrödinger's equation for the Hydrogen atom as the basic mathematical model of quantum mechanics.

In another 1905 article Einstein assigned the Lorentz transformation a physical meaning, which Lorentz had said would not make any sense, and so formed his Special Theory of Relativity SR.

Einstein thus contributed to the formation of modern physics in 1905 by attributing physical meanings to both Planck's quantum $h\nu$ and the Lorentz transformation, in direct contradiction to both Planck and Lorentz.  

As time went on and the authority of Planck and Lorentz faded, Einstein's ideas about physicality of photons and the Lorentz transformation slowly gained support, but when they became the standard of the new Quantum Mechanics of Bohr-Born-Heisenberg-Dirac in the 1930s, then Einstein said: Stop, QM is no longer real physics!  Only Schrödinger said the same thing, but both were efficiently cancelled by Bohr. 

Einstein thus started out and ended as a tragic figure. First he genuinely misunderstood Planck and

Lorentz about physical reality and so contributed the development of a new form of physics, which he on good grounds criticised for lacking physicality. The irony was that physicists listened when he was wrong but not when he was right.   

The Secret of $E=h\nu$ as Smallest Quanta of Energy/Action

Quantum Mechanics was born from the smallest quantum of energy (or action) $h\nu$, with $h$ Planck's constant and $\nu$ a frequency, appearing in Planck's mathematical analysis of blackbody radiation which captured the dependence on temperature $T$ and $\nu$ of the energy transfer $E$ from a glowing body in the form of Planck's Law 

• $E(\nu, T)=\gamma T\nu^2\times C(\alpha )$ with $\gamma =\frac{2k}{c^2}$,     (1)

where $k$ is Boltzmann's constant and $c$ the speed of light, and 

• $C(\alpha )=\frac{\alpha}{\exp^\alpha-1}$ with $\alpha =\frac{h\nu}{kT}$ 

is a high-frequency cut-off  factor with activation if $h\nu >kT$.   

The analysis concerned a hypothetical blackbody as a cavity with reflecting walls filled with waves of many frequencies brought to a common temperature by the presence of a small piece of sooth.

Planck determined a value of $h=6.55\times 10^{-34}$ Jouleseconds to make his Law fit with observation of the cut-off factor $C(\frac{h\nu}{kT})$ with $\nu$, $k$ and $T$ given.  

The smallest quantum of energy/action $h\nu$ was used as a "mathematical trick" to get a the observed dependence of the high-frequency cut-off factor on $\frac{\nu}{T}$ as an expression of Wien's displacement law. No real physics. Not yet any atom.

The next step was Einstein's association of the smallest quantum of energy/action $h\nu$ to exactly one "particle of light" of frequency $\nu$ later named "photon", in his 1905 heuristic analysis of the photo-electric effect as "one electron - one photon". No real physics. Not yet any atom. Einstein formally identified the energy $E$ of one electron through $E=h\nu$, but he did not yet have any model of an electron. 

In 1913 Bohr presented a model of a Hydrogen atom as one electron revolving around a kernel in different possible orbits of with certain specific energies, with differences $E$ of these possible one-electron energies showing to fit with the observed frequencies $\nu$ of the radiation spectrum of Hydrogen if the shift/jump of one electron was assigned an energy $E=h\nu$. Success, but an ad hoc model of an electron without physics with an ad hoc assignment of exactly the energy $E=h\nu$ to the jump of one electron between the two energy levels.   

In 1926 Schrödinger presented a wave equation model of a Hydrogen atom in terms of a wave function representing electron charge density with eigenvalues coinciding with the energy levels of the Bohr model. Again with an ad hoc association of the energy $E=h\nu$ to one electron shifting between energy levels differing by $E$. Great success in the form of a classical continuum model, but the generalisation to atoms with more than one electron carried physics into the new modern world of quantum physics fundamentally different from continuum physics with Planck's constant $h$ setting a form of smallest scale requiring quantisation of physics. We sum up:

The secret of Planck's constant $h$ with $h\nu$ smallest quantum of energy/action.  

1. A value of $h$ is determined to make the high frequency cut-off depending on $\frac{h\nu}{kT}$ in Planck's Law of blackbody radiation, fit with observation.
2. The value of $h$ so determined is connected to Schrödinger's Equation SE for a Hydrogen atom with one electron in the following way. The eigenvalues of SE represent different possible energies of the electron and differences $E$ between energy levels represent shifts of energy $E$ of one electron, which in SE is assigned a frequency $\nu = \frac{E}{h}$ so that $E=h\nu$. 
3. The shift between energy levels of the one electron of the Hydrogen atom $E=h\nu$ is associated with emission/absorption of one photon of frequency $\nu$ carrying an energy of $h\nu$. 

Altogether we understand that Planck's constant $h$ is determined to make the high-frequency cut-off in Planck's Law fit with observation. This value is then used to assign the energy $E=h\nu$ to one photon corresponding to the jump of one electron of a Hydrogen atom between energy levels differing by $E$.

We understand that high-frequency cut-off is related to small-wavelength cut-off as condition on spatial resolution as discussed in detail in Computational Blackbody Radiation. 

To understand that the smallest quantum of energy/action $E=h\nu$ is a definition without physical representation, it helps to recall that $h$ in the 2019 SI specification of units is assigned the exact value $6.62607015\times 10^{-34}$, which differs from Planck's original value $6.55 \times 10^{-34}$. If $h\nu$ really carried some real physics, it would not make sense to assign it a specific value, since it does not make sense to prescribe real physics how to behave. Ok?

PS1 A basic difficulty of understanding theoretical physics is that the distinction beween definition and physical fact is often blurred. If you do not understand that the speed of light in vacuum and smallest quantum of energy are assigned certain values rather than being given by the Creator, you miss something very essential.

PS2 The central theme in all the above models is the radiating atom in radiative equilibrium with light of certain frequencies showing up in the emission or absorption spectrum of the atom, as a resonance phenomenon analysed in Computational Blackbody Radiation. The basic mathematical model takes the following form in a wave function $\phi (t)$ depending on time $t$ satisfying

• $\ddot\phi -\nu^2\phi -\gamma\dddot\phi = f$           (2)

where a dot signals differentiation with respect to a time variable, and $f$ is forcing with frequency $\tilde\nu\approx \nu$ in near resonance and $\gamma <<\frac{1}{\nu^2}$. The essence of radiative equilibrium as output = input reads (in terms of time averages)

• $\gamma\ddot\phi^2 =\gamma T \nu^2 = f^2$,          (3)
• $T = \dot\phi^2+\nu^2\phi^2$. 

Here $T$ represents temperature for a macroscopic body, while for a single atom rather $T\sim N$ with $N$ number of electrons. The 

Planck's Law connects the differences of discrete electronic energy levels $E=h\nu$ of an atom in radiative equilibrium with light of frequency $\nu$ appearing in the emission/absorption spectrum of the atom as isolated atom or as part of a macroscopic body, with $h$ acting like a constant connecting energy with frequency.  

Planck's Faustian Deal: The Quantum

Here is a short excerpt from my book Dr Faustus of Modern Physics giving perspective on the birth in 1900 of Quantum Mechanics with Planck's mathematical analysis of blackbody radiation introducing $E=h\nu$ as a smallest quantum of energy. 

To boost his career and the science of the booming German Empire, Max Planck, professor at the University of Berlin with a background from thermodynamics, took on the main open problem of physics at the end of the 19th century, namely to explain why the ultra-violet catastrophe of blackbody radiation predicted by classical theoretical physics cannot be observed. At stake was the credibility of a science of physics (and the German Empire) predicting very intense high-frequency radiation which simply refused to exist. The stakes were thus very high and Planck with ambition stepped in:

• The whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 

The price was to give up his soul as very serious scientist with deep conviction to classical ideals, which paved the way for new quantum physics giving up classical principles of reality, causality and determinism, now in deep crisis.  

1. Nobel Prize to Planck

 The Nobel Prize in Physics 1918 was awarded (in 1919) to Max Planck:

• in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta.

It took the Nobel Committee more than 10 years to come to this conclusion, because Planck’s new concept of a smallest quantum of energy was so difficult to swallow, described by the Swedish mathematician Ivar Fredholm as “hardly plausible”. In 1918 the Committee gave in under pressure to give the prize to Bohr and Einstein, which required a prize to Planck first. The presentation speech by Ekstrand stated:

• Planck’s radiation theory is, in truth, the most significant lodestar for modern physical research, and it seems that it will be a long time before the treasures will be exhausted which have been unearthed as a result of Planck’s genius.
• Planck constant, proved, as it turned out, to be of still greater significance: The product $h\nu$, where $\nu$ is the frequency of vibration of a radiation, is actually the smallest amount of heat which can be radiated at the vibration frequency $\nu$. This theoretical conclusion stands in very sharp opposition to our earlier concept of the radiation phenomenon.

Planck was thus viewed as having “discovered” a physical phenomenon of “energy quanta”, which in fact was a “theoretical conclusion”. This contradiction has come to form the ideology of modern physics made possible by breaching the classical holy distinction between reality and mathematical model.

2. Planck's Confession

From Planck's self-biography:

• We shall now derive strange properties of heat radiation described by electromagnetic wave theory.
• ..the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 
• Either the quantum of action was a fictional quantity, then the whole deduction of the radiation law was essentially an illusion representing only an empty play on formulas of no significance, or the derivation of the radiation law was based on sound physical conception. Mechanically, the task seems impossible, and we will just have to get used to it (quanta). 
• My futile attempts to fit the elementary quantum of action into classical theory continued for a number of years and cost me a great deal of effort. Many of my colleagues saw in this something bordering on a tragedy (Planck shortly before his death).
• I tried immediately to weld the elementary quantum of action somehow in the framework of classical theory. But in the face of all such attempts this constant showed itself to be obdurate...
• My futile attempts to put the elementary quantum of action into the classical theory continued for a number of years and they cost me a great deal of effort.
• The assumption of an absolute determinism is the essential foundation of every scientific inquiry.
• All matter originates and exist only by virtue of a force which brings the particle of an atom to vibration and hold this most minute solar system of the atom together. We must assume behind the existence of this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter...
• In order to find the correct resonator entropy S it must be assume that the energy U of a resonator with frequency ν can only take on discrete energy values, to wit, integer multiples of h times ν, in contrast to classical theory where U can be any multiple, integer or not, of ν. We now say that U is quantised.
• My maxim i always this: consider every step carefully in advance, but then, if you believe you can take the responsibility for it, let nothing stop you.
• For by nature I am peaceful and disinclined to questionable adventures...for unfortunately I have not been given the capacity to react quickly to intellectual stimulation.

3. Planck on Politics

Planck lost his son Karl in combat during 1st World War and his son Erwin was executed after a plot against Hitler at the end of the 2nd World War. Planck signed together with 93 German intellectuals the Appeal to the Cultured Peoples of the World on 4 October 1914:

• We declare the leaders of German art and science to be at one with the German army.

Planck reports as Rector of Berlin University in 1914:

• The German people ha found itself again. One thing only we know, that we members of our university...will stand together as one man and hold fast until - despite the slander of our enemies - the entire world comes to recognise the truth and German honor.
• But we shall also see an feel how, in the fearful seriousness of the situation, everything that a country could call its own in physical and moral power came together with the speed of lightning and ignited a flame of holy wrath blazing to the heavens, while so much that had been considered important and desirable fell to the side, unnoticed, as worthless frippery.